{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:I7FR7DESYT5FLUXP5UPCVLCUYH","short_pith_number":"pith:I7FR7DES","schema_version":"1.0","canonical_sha256":"47cb1f8c92c4fa55d2efed1e2aac54c1df7b77534dae01dc60aecacd871d8693","source":{"kind":"arxiv","id":"1703.06047","version":2},"attestation_state":"computed","paper":{"title":"Exact distance coloring in trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ararat Harutyunyan, Louis Esperet, Nicolas Bousquet, R\\'emi de Joannis de Verclos","submitted_at":"2017-03-17T15:06:03Z","abstract_excerpt":"For an integer $q\\ge 2$ and an even integer $d$, consider the graph obtained from a large complete $q$-ary tree by connecting with an edge any two vertices at distance exactly $d$ in the tree. This graph has clique number $q+1$, and the purpose of this short note is to prove that its chromatic number is $\\Theta\\big(\\tfrac{d \\log q}{\\log d}\\big)$. It was not known that the chromatic number of this graph grows with $d$. As a simple corollary of our result, we give a negative answer to a problem of van den Heuvel and Naserasr, asking whether there is a constant $C$ such that for any odd integer $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.06047","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-17T15:06:03Z","cross_cats_sorted":[],"title_canon_sha256":"671495fa42eb183b29499445df0abe84e4e361525c151138e3ebe579f3890e92","abstract_canon_sha256":"4c21d7c66eff15d1e6683fa24df706d9767d0b0195094c8da096fbe234d11b93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:14.912279Z","signature_b64":"aBjqXTJN6Uubo5+dUBzKW+3TisBhT9Rkm8yqdxZihaj/EPsC+t7iOww/uVH8MdUaPD8HQBt/3Ohfd/mN0RXGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47cb1f8c92c4fa55d2efed1e2aac54c1df7b77534dae01dc60aecacd871d8693","last_reissued_at":"2026-05-17T23:51:14.911640Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:14.911640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact distance coloring in trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ararat Harutyunyan, Louis Esperet, Nicolas Bousquet, R\\'emi de Joannis de Verclos","submitted_at":"2017-03-17T15:06:03Z","abstract_excerpt":"For an integer $q\\ge 2$ and an even integer $d$, consider the graph obtained from a large complete $q$-ary tree by connecting with an edge any two vertices at distance exactly $d$ in the tree. This graph has clique number $q+1$, and the purpose of this short note is to prove that its chromatic number is $\\Theta\\big(\\tfrac{d \\log q}{\\log d}\\big)$. It was not known that the chromatic number of this graph grows with $d$. As a simple corollary of our result, we give a negative answer to a problem of van den Heuvel and Naserasr, asking whether there is a constant $C$ such that for any odd integer $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06047","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.06047","created_at":"2026-05-17T23:51:14.911736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06047v2","created_at":"2026-05-17T23:51:14.911736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06047","created_at":"2026-05-17T23:51:14.911736+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7FR7DESYT5F","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7FR7DESYT5FLUXP","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7FR7DES","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH","json":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH.json","graph_json":"https://pith.science/api/pith-number/I7FR7DESYT5FLUXP5UPCVLCUYH/graph.json","events_json":"https://pith.science/api/pith-number/I7FR7DESYT5FLUXP5UPCVLCUYH/events.json","paper":"https://pith.science/paper/I7FR7DES"},"agent_actions":{"view_html":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH","download_json":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH.json","view_paper":"https://pith.science/paper/I7FR7DES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06047&json=true","fetch_graph":"https://pith.science/api/pith-number/I7FR7DESYT5FLUXP5UPCVLCUYH/graph.json","fetch_events":"https://pith.science/api/pith-number/I7FR7DESYT5FLUXP5UPCVLCUYH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH/action/storage_attestation","attest_author":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH/action/author_attestation","sign_citation":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH/action/citation_signature","submit_replication":"https://pith.science/pith/I7FR7DESYT5FLUXP5UPCVLCUYH/action/replication_record"}},"created_at":"2026-05-17T23:51:14.911736+00:00","updated_at":"2026-05-17T23:51:14.911736+00:00"}